Full field photoelastic stress analysis

ABSTRACT

A structural specimen coated with or constructed of photoelastic material, when illuminated with circularly polarized light will, when stressed; reflect or transmit elliptically polarized light, the direction of the axes of the ellipse and variation of the elliptically light from illuminating circular light will correspond to and indicate the direction and magnitude of the shear stresses for each illuminated point on the specimen. The principles of this invention allow for several embodiments of stress analyzing apparatus, ranging from those involving multiple rotating optical elements, to those which require no moving parts at all. A simple polariscope may be constructed having two polarizing filters with a single one-quarter waveplate placed between the polarizing filters. Light is projected through the first polarizing filter and the one-quarter waveplate and is reflected from a sub-fringe birefringent coating on a structure under load. Reflected light from the structure is analyzed with a polarizing filter. The two polarizing filters and the one-quarter waveplate may be rotated together or the analyzer alone may be rotated. Computer analysis of the variation in light intensity yields shear stress magnitude and direction.

CROSS REFERENCES TO RELATED APPLICATIONS

This is a continuation of U.S. Ser. No. 08/867,475, now U.S. Pat. No.6,055,053 entitled Full Field Photoelastic Stress Analysis filed Jun. 2,1997 which is incorporated herein by reference.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSOREDRESEARCH AND DEVELOPMENT

The U.S. Government has a paid-up license in this invention and theright in limited circumstances to require the patent owner to licenseothers on reasonable terms as provided for by the terms of Contract No.NAS 1-97036 awarded by the National Aeronautics and SpaceAdministration.

BACKGROUND OF THE INVENTION

The present invention relates to apparatus and methods for detectingstrain in objects in general, and apparatus and methods employingphotoelastic techniques to detect strains indicative of shear stressesin particular.

Proper design of a load carrying structure requires attention to thecost, weight, and durability of the structure. Effective design requiresan understanding of the loads and deflection which the structureundergoes during its lifetime. With highly engineered parts the veryfeasibility of a machine or structure may require advanced designtechniques.

Computer based mathematical structural models of structures, such asthose employing Finite Element Analysis (FEM), are widely used to helpthe designer simulate structures and imposed loads. While often helpful,a mathematical model is only as good as the correlation between themodel equations and the real world. To test this correlation, designersmust fabricate real parts and subject them to physical loads. Theresults of experiments on real world test structures are used to improvethe mathematical models. Comparison of the physical results to thosepredicted by the mathematical model aids the designed in developingequations and constants which more closely model the real world.

The classical approach to determining stresses within a structure in thereal world is to apply strain gauges to the object and measure theinduced strains when the structure is loaded. Strain gauges, whileaccurate, provide information only about a limited number of points onthe structure and do not allow easy visualization of the stressesproduced in a structure.

Recently, new techniques that allow rapid capture of full field stressesover the surface of an entire structure or portion of a structure havebeen developed. These techniques such as Thermoelastic Stress Analysis(TSA) have allowed tension and compression loads to be rapidlydetermined for every point on a structure. These new techniques allowvisualization of the imposed strains and displacement in objects beingtested.

The structural analysis technique known as Photoelastic Stress Analysis(PSA) has been recognized as having great potential because it can beused to determine shear stresses within a structure directly.

Thermoelastic Stress Analysis detects minute changes in temperature dueto compression or expansion of a structure. Expansion and compressioncorrespond to tensile and compressive forces within a structure. Shearstresses must be derived from a knowledge of the observed tensile andcompressive forces. Photoelastic Stress Analysis which can providedirect imaging of shear stresses thus provides the missing ingredient tocomplete characterization of a loaded structure. In additionPhotoelastic Stress Analysis can be performed by statically loading astructure. In many cases statically loading a structure will besignificantly less costly than the dynamic loading required forThermoelastic Stress Analysis. Maximum understanding of a structure isachieved by employing both TSA and PSA.

PSA is based on the observation that some materials respond to stress byincreasing the speed of light through the material along the plane ofthe imposed stress. The orientation of the increased speed of light isreferred to as the fast axis. A slow axis is defined perpendicular tothe fast axis. Where the principal stresses are unequal in magnitude, ordiffer in sign, such materials exhibit birefringence. Birefringence is aproperty of an optically transparent material which causes the velocityof light through the material to vary depending on the vibrational planeof the light. The amount of birefringence present in an object isproportional to the difference between the principal stresses, whichdefines the shear stresses within the object. To apply PhotoelasticStress Analysis techniques, a test model must be constructed of, orcoated with, a birefringent material.

When plane polarized light from a first polarizer passes through abirefringent material in which the fast axis is tilted with respect tothe axis of the polarized light, the polarized light is resolved intotwo perpendicular components, a first component along the fast axis anda second component along the slow axis, thereby producing two componentsof the linearly polarized light which are separated in time. When thefast axis and slow axis components are viewed through a secondpolarizing filter, referred to as an analyzer, which is arrangedperpendicular to the orientation of the first polarizer, a component ofeach of the first and second components will be able to pass through thesecond polarizing filter or analyzer. Because the first and secondcomponents which pass through the birefringent material are separated intime they are not fully recombined by the analyzer but each component isresolved into a portion which is parallel to the analyzer and thus canpass through the analyzer.

This type of optical system employing two orthogonally oriented planepolarizing filters: a polarizer and an analyzer, is known as a darkfield plane polariscope. Any birefringence exhibited by the objectplaced between the crossed polarizing filters results in light passingthrough the polariscope. A similar device uses plane polarizing filterswhich are oriented with their planes of polarization parallel, and isreferred to as a bright field linear polariscope. The presence of abirefringent object between the parallel polarizing filters results insome light not passing through the filters.

Loading of an object can create induced birefringence, which, whenviewed through the plane polariscope, forms two sets of fringes. Thefirst set of fringes, referred to as isoclinics, demarcate portions ofthe object where one of the principal stress directions is parallel tothe axis of the polarizer. The second set of fringes, referred to asisochromatics, demarcate portions of the object where the difference ofthe principal stresses is zero or where the stress is of sufficientmagnitude to retard the transmission of light by a whole number ofwavelengths.

The isochromatic fringes may be viewed alone by eliminating theisoclinic fringes by passing the beam through a circular polariscope.

A circular polariscope consists of two polarizing filters and twoone-quarter waveplates positioned between the polarizing filters. Againthe polarizing filters may be arranged so that the planes ofpolarization are parallel, to produce a light field polariscope, or areperpendicular, to produce a dark field polariscope.

The isoclinic fringes are eliminated because the first one-quarterwaveplate produces circularly polarized light in which the light nolonger has a single axis of polarization, instead the axis ofpolarization rotates. The second one-quarter waveplate converts the beamback into linearly polarized light.

Photoelastic stress analysis suffers from a number of limitations whichlimit its usefulness. In order for the technique to be applied to astructure the structure must be constructed of a birefringent materialor coated with a birefringent coating of a known thickness.

Constructing the structure of birefringence materials, which forpractical reasons are typically low strength plastics, have inherentlimitations when attempting to verify the structural response of highstrength metals and composite structures. On the other hand, applying acoating to a structure has in the past required molding a layer ofphotoelastic plastic to the shape of the structure and then bonding thephotoelastic layer to the structure. This technique is time consumingand requires considerable skill to avoid pre-stressing the plasticlayer. Other techniques of coating the structure such as spraying orpainting result in an uneven coating. Any nonuniformity in the coatingthickness results in a proportional error in the measured stresses.Further spray on coating result in insufficient birefringence to applyclassical photoelastic techniques with reasonable resolution.

Another problem with photoelastic stress analysis is that to determinestress at a particular point the number of fringes between a nonstressed portion of the structure and the particular point must becounted. This makes the determination of the magnitude of the stressesin the structure subject to errors in counting the fringes or choosing astarting point for counting the fringes. The difficulty in accuratelycounting the number of fringe lines present can be overcome by choosingthe thickness of the coating so the stresses produce less then a singlefringe.

With this technique the changes in stress levels are represented by abrightness intensity within a single fringe band. However, knowntechniques for viewing the stress induced brightness level can notreadily distinguish between minimum and maximum axes of stress.

What is needed is a photoelastic coating technique and a photoelasticanalyzing technique and apparatus which produces full fielddetermination of shear stress magnitude and direction.

SUMMARY OF THE INVENTION

A structural specimen coated with or constructed of photoelasticmaterial, when illuminated with circularly polarized light will, whenstressed; reflect or transmit elliptically polarized light, thedirection of the axes of the ellipse and variation of the ellipticallypolarized light from illuminating circular polarized light willcorrespond to and indicate the direction and magnitude of the shearstresses for each illuminated point on the specimen.

The principles of this invention allow for several embodiments of stressanalyzing apparatus, ranging from those involving multiple rotatingoptical elements, to those which require no moving parts at all. Therotating optic apparatus will be discussed first, with the conceptuallymore advanced non-moving part devices discussed later.

A simple polariscope may be constructed having two polarizing filterswith a single one-quarter waveplate placed between the polarizingfilters. Light is projected through the first polarizing filter and theone-quarter waveplate and is reflected from a sub-fringe birefringentcoating on a structure under load. Reflected light from the structure isanalyzed with a polarizing filter. The two polarizing filters and theone-quarter waveplate may be rotated together or the analyzer alone maybe rotated.

An image of the structure taken through the polariscope can be capturedby a camera and analyzed by a computer. For each rotation of thepolariscope each pixel in the image corresponding to a location on thestructure shows a time dependent light curve with minimum and maximumintensity which exhibits a frequency twice that of the rotation rate ofthe polariscope. The maximum intensity correlates with the maximumstress amplitude. The phase angle between a reference position of thepolariscope and the maximum and minimum intensity positions defines theorientation of the axes of maximum and minimum shear stress.

In order to observe birefringence on a structure under load abirefringent coating of known thickness must be applied to the structurebefore it is loaded.

Two techniques are disclosed. The first technique employs a spray-oncoating which contains a known amount of one or more dyes. The coatingas modified by the dyes produces known but differing attenuation of eachof to three selected wavelengths of light. The structure is illuminatedwith white light or light containing all three wavelengths. And thethickness of the coating is derived from the relative attenuation of thedifferent wavelengths of light.

The second technique utilizes a transparent oxide such as a clearanodized coating on aluminum. If the chemical process used to producethe coating inherently produces a coating of uniform thickness,measuring the coating thickness is not necessary.

It is a feature of the present invention to provide an apparatus and atechnique for determining full field shear stresses in an objectsubjected to a load.

It is a further feature of the present invention to provide an apparatusfor using photoelastic methods which requires no moving parts and can becalibrated and aligned in software.

It is another feature of the present invention to provide a polariscopewhich can determine the orientation of the principal axes of stress ofan illuminated specimen.

It is a further feature of the present invention to provide an aid forthe design of structures which does not require a load frame capable ofcyclical loading of the structure.

It is a still further feature of the present invention to provide acoating and coating method which improves accuracy and costeffectiveness for photoelastic stress analysis.

It is a yet further feature of the present invention to provide aphotoelastic coating which does not relax over time.

It is a yet further feature of the present invention to provide a newtechnique for determining shear stress direction and magnitude byutilizing the principles of photoelasticity.

Further objects, features and advantages of the invention will beapparent from the following detailed description when taken inconjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a stress analyzing optical path of aphotolastic stress analyzer of this invention for use with a lighttransmissive specimen.

FIG. 2 is a schematic view of a stress analyzer of this invention foruse with a light reflective specimen.

FIG. 3 is a schematic view of the light intensity variation produced bya conventional plane polariscope.

FIG. 4 is a schematic view of the light intensity variation produced bythe grey field polariscope of FIGS. 1 and 2.

FIG. 5 is a schematic view of the relative orientation of thebirefringent axes of the offset plate with respect to the polarizer andthe analyzer of FIG. 1.

FIG. 6 is a schematic view of the characteristic of light as it transitsat each position along the stress analyzer of this invention.

FIG. 7 is a simplified schematic view of stress analyzer of FIG. 2.

FIG. 8 is a schematic view of alternative embodiment stress analyzer ofFIG. 2 wherein the one-quarter waveplate is placed adjacent to theanalyzer.

FIG. 9 is a schematic view of a further alternative embodiment stressanalyzer of this of this invention having folded light path.

FIG. 10 is a schematic view of a still further alternative embodimentstress analyzer of this invention similar to FIG. 2 but for use with atransparent specimen.

FIG. 11 is a schematic view of an additional alternative embodimentstress analyzer of this invention similar to FIG. 8 but for use with atransparent specimen.

FIG. 12 is a schematic view of yet another alternative embodiment stressanalyzer of this invention for use with a transparent specimen employingan optical system similar to FIG. 9.

FIG. 13 is a cross-sectional view of an aluminum test specimen with analuminum oxide birefringent coating developed thereon.

FIG. 14 is an enlarged cross-sectional view of a test specimen with aspray-on coating of birefringent material which differentially absorbsred, blue, and green light.

FIG. 15 is a top plan view of a grey field polariscope without movingcomponents.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring more particularly to FIGS. 1-15 wherein like numbers refer tosimilar parts, a grey field polariscope 20 is shown in FIG. 1. The greyfield polariscope 20 has three optical elements: a first planepolarizing filter or polarizer 22, a second plane polarizing filter oranalyzer 24, and a one-quarter offset waveplate 26 positioned betweenthe polarizer 22 and the analyzer 24. The three optical elements may beall mechanically or electrically linked so as to rotate together at aconstant angular velocity ω, however only the analyzer 24 is required torotate. A specimen 28 which exhibits birefringence due to an imposedload is positioned between the offset waveplate 26 and the analyzer 24.

A structural specimen 28 is constructed of photoelastic material and isilluminated with circularly polarized light created by passing polarizedlight through the quarter waveplate 26. When the specimen is stressed itwill transmit elliptically polarized light the variation in lightintensity from the grey field and orientation of the axes of which willcorrespond to and indicate the maximum shear stress and the orientationof the principal stresses for each illuminated point on the specimen.

A minimum delay axis is defined for a birefringent material along whichlight passes through the material with minimum delay. Along an axisperpendicular to the axis of minimum delay light is subjected to themaximum retarding effect.

Index of refraction is defined as the ratio between the speed of lightin a vacuum and the speed of light in a material. In certain materialsthe index of refraction, that is, the speed with which light travelsthrough the material, depends on the orientation of the vibrationalplane of the light with respect to orientation of the atoms making upthe material. For example when ordinary light passes through a calcitecrystal along a particular crystallographic axis the strongbirefringence exhibited by the crystal resolves the light into twopolarized images. These images are spatially separated as the lightwhich is experiencing the higher index of refraction experiences greaterrefraction.

Birefringent materials of interest for photoelastic stress analysisrespond to stress by exhibiting birefringence where the index ofrefraction is minimized and the speed of light is maximized for lightvibrating in a plane parallel to the axis of maximum applied stress. Theaxis of minimum normal stress is oriented 90 degrees from the axis ofmaximum applied stress and light vibrating in a plane parallel to theminimum normal stress is retarded with respect to light travelingparallel to the axis of maximum applied stress.

A birefringent material resolves any light passing through it into twopolarized orthogonal components which are separated in time from eachother. If two polarizers such as shown in FIG. 1 are considered withoutthe one-quarter waveplate 26 they would constitute a dark fieldpolariscope because the polarizers 22 and 24 are arranged with theiraxes of polarization 30, 32 perpendicular to each other and if there areno birefringent elements between them, no light will pass through bothpolarizers.

When a birefringent specimen 28 having a fast axis σ₁ and a slow axis σ₂is interposed between the elements of a conventional dark field,polarized light parallel to the axis 30 will be resolved into acomponent lying along the fast axis σ₁ and a component lying along theslow axis σ₂. Because the two components are separated in time they arenot fully recombined at the analyzer 24 but are instead resolved by theanalyzer into a component of light parallel to the analyzer axis 32which then passes through the analyzer 24.

A typical birefringent specimen as used in conventional photoelasticstress analysis, will under even moderate loading produce a differencein the apparent length of the light path through the specimen of manywavelengths of light. Because the phenomenon we are dealing with dependsonly on the phase difference between the light traveling along the slowaxis and along the fast axis the brightness of a point on the specimenis not affected by the whole number of wavelengths in apparent pathlength between the slow and fast axes of the specimen.

As the stress increases at a particular point the phase angle betweenlight traveling along the slow axis and the fast axis in the specimenwill reach a maximum when the two waveforms are 180 degrees out ofphase. By keeping the total birefringence to less then one-half awavelength of light, brightness of a point on a specimen correlates toabsolute stress magnitude. And, as discussed below, when using aone-quarter waveplate it will be desirable to keep the totalbirefringence to one-quarter of a wave or a phase difference of ninetydegrees.

In most circumstances for a light transmissive specimen, keeping thetotal birefringence to less that a quarter of a wavelength of light isimpractical. However by using a thin birefringent coating on a specimenit is possible to keep the total birefringence to one-quarter of awavelength. Furthermore, by using the techniques of this invention, itis possible to image birefringent specimens with multiple wavelengths ofinduced birefringence. For simplicity of discussion the case of atransmission specimen with total birefringence of less than one-quarterwavelength is discussed before turning to more practical embodiments ofmy invention.

As shown in FIG. 1, two polarizers arranged with perpendicular axes ofpolarization constitute a plane polariscope. In a plane polariscope boththe polarizer 22 and the analyzer rotate together. If the elements of aplane polariscope are rotated, each point on the specimen 28 will appearwith maximum brightness when the axis 32 of the analyzer is orientedforty-five degrees from to the fast axis σ₁ or the slow axis σ₂ whichangular position will occur twice for each axis as the analyzer isrotate for a total of four times (4ω) for each rotation of the polarizerand the analyzer. If the specimen has only sufficient birefringence tocreate less than one-quarter wavelength of light retardation, the levelof stress within the object 28 will be viewable as a brightness level.

FIG. 3 illustrates the pattern of light intensity visible for aparticular location on a specimen as the polarizer and analyzer of aplane polariscope are rotated once. The intensity of light visiblethrough the analyzer is depicted by the four lobed curve 34. Each timethe slow axis or the fast axis of a particular point on the specimen isaligned halfway between the axis 30 of the polarizer and the axis 32 ofthe analyzer the separation of light coming through the polarizer 22into two time-separated components is maximized. The following EquationOne describes the intensity of a point on the specimen as a planepolariscope is rotated.

I=a ²sin(Δ/2)sin²(2α)

I is the intensity of light at a selected point on the specimen

a is the amplitude of the source

α is the angle between the polarizer and the direction of principalstresses

Δ represents the relative retardation due to birefringence in thespecimen

Only α changes as a plane polariscope rotates, the relative retardation,Δ due to birefringence in the specimen is related to the state of stressof a point on the specimen and does not change for a given loadcondition. Intensity of light I is therefore maximized when 2α ismaximized, which, for the sine function, occurs when α equals forty-fivedegrees. Because the sine term is squared the maximum occurs in eachquadrant leading to the four lobed brightness pattern 34. The curve 34indicates that the orientation of the principal axes of stress from aknown angular position 36 can be determined with the plane polariscopebut that it is not possible to differentiate between the maximum andminimum shear axes. This is because the slow axis σ₂ and the fast axisσ₁ have the same effect of separating light which passes through thepolarizer 22 into its two components which allows light to pass throughthe analyzer 24.

If the polariscope 20 in FIG. 1 is considered with just the polarizer22, the one-quarter waveplate 26, and the analyzer 24, the effect on thewaveplate 26 when oriented forty-five degrees from the polarization axes30, 32 on the light which passes through the polariscope 20 can bepredicted from equation one.

The partial waveplate 26 will have maximum effect when orientedforty-five degrees from the polarization axes. The effect will be toproduce a neutral grey field as viewed through the analyzer 24. With thepartial waveplate so oriented, maximal stresses will have increasedbrightness whereas minimal stresses will have decreased brightnessallowing them to be differentiated.

The waveplate introduces a birefringence of one-quarter of a wavelengthof light between a fast axis F and a slow axis S.

The intensity of light of the grey field polariscope 20 is described byfollowing equation:$I = {\frac{a^{2}}{2}\left( {1 + {\sin \quad {\Delta sin2\theta}}} \right)}$

I is the intensity of light at a selected point on the specimen

a is the amplitude of the source

θ=is the position of the analyzer relative to the fast axes

Δ represents the relative retardation due to birefringence in thespecimen

Circularly Polarized Light

The physical effect of the partial waveplate 26 is to produce circularlypolarized light. Circularly polarized light is plane polarized lightwhere the plane of polarization rotates about a line parallel to thedirection of propagation of the light. Circularly polarized light canalso be thought of as polarized light where the orientation of the planeof polarization has a probability function evenly distributed about thedirection of propagation of the light. Thus when circularly polarizedlight is viewed through the analyzer 24, only a component of thecircularly polarized light will pass through the analyzer 24, producingthe neutral grey observed.

Because the plane of polarization is rotating, the polarizer and the onequarter waveplate do not need to rotate in order to produce the lightpattern of FIG. 4. Only the analyzer is required to rotate.

When planar polarized light encounterers a second plane polarizingfilter the intensity of light which passes through the second filter isproportional to the cosine of the angle between the axis of thepolarized light and the axis of the polarizing filter. When circularlypolarized light encounterers a plane polarizing filter, the amount oflight which passes through the polarizing filter is independent of theorientation of the filter and can be viewed as the summation of allpossible orientations times the cosine between each possible orientationand the axis of the polarizing filter. This results in the same lightintensity as if the circularly polarized light were planar polarized andoriented forty-five degrees from the axis of the polarizing filter.

The effect of passing circularly polarized light through a birefringentobject is to produce elliptically polarized light. Ellipticallypolarized light has a rotating axis of polarization which changes inmagnitude as it rotates. The amount of elliptically polarized lightwhich will pass through a plane polarizing filter depends on theorientation of the major axis of the ellipse with respect to the axis ofthe plane polarizing filter. The shape of the ellipse, or eccentricityof the ellipse, is dictated by the difference between the major andminor axes of stress, while the orientation of the major axis indicatesthe direction of those stresses. By determining the shape andorientation of the ellipse the magnitude and direction of the principalstresses σ₁ and σ₂ is determined.

Another Approach to Understanding

Another approach to understanding how this determination of themagnitude and direction of the principal axes of stress comes is asfollows. When a birefringent specimen 28 is analyzed with thepolariscope 20 including the one-quarter waveplate 26 the brightness ofa particular point will only reach maximum brightness twice for eachrotation of the polariscope 20, as shown in FIG. 4. The maximumbrightness of a point on the specimen 28, in the absence of theone-quarter waveplate, occurs when the fast axis or slow axis of thespecimen 28 is halfway between the axes 30, 32 of polarization of thepolarizer 22 and the analyzer 24.

The one-quarter waveplate is also oriented halfway between the axes 30,32 of the analyzer 22 and polarizer 24; as the polariscope rotates, thefast axis of the one-quarter waveplate will pass through the fast axisof the specimen 28 just as the fast axis of the specimen is alsooriented at forty-five degrees to the axis of the analyzer 22 andpolarizer 24 and showing maximum brightness. Thus the effect of theone-quarter waveplate 26 is to increase the brightness maximum caused bythe principal or fast axis of the specimen 28.

Contrarily, when the slow axis of the specimen 28 is positioned formaximum brightness, halfway between the axes of the polarizer 22 and theanalyzer 24, the fast axis of the one-quarter way plate will besuperimposed on the slow axis of the specimen and the net effect will beto minimize the brightness of a point on the specimen 28.

Utilizing the polariscope 20 of FIG. 1, the brightness maximum willcorrelate to the square of the maximum stress amplitude, and thebrightness minimum will correspond to the square of the minimum stressamplitude. The location of the maximum and minimum stress axes can bedetermined by the orientation of the maximum and minimum lightamplitudes with respect to a reference position 36 as shown in FIG. 4.

Because the one-quarter waveplate introduces circularly polarized light,only the analyzer is required to rotate if the one-quarter waveplate isposition in the light path before the light reaches specimen. However tominimize irregularities in the optical elements it may be desirable forpractical devices to rotate all three elements, the polarizer, theone-quarter waveplate, and the analyzer.

Further Consideration of Circularly and Elliptically Polarized Light

Referring to FIG. 6, the steps whereby light passing through aphotoelastic material is used to determine with the aid of a grey fieldpolariscope the shear stresses in the material is depicted. Light from alight source 36 passes through a plane polarizer 22. The resulting light38 vibrates in a single plane. The light 38 then passes through aone-quarter waveplate 26 which is oriented with the fast axis F inclinedforty-five degrees from the orientation of the polarizer 22. Thisresults in the orientation of the planar light 38 rotating in time andspace as the light propagates forward.

Circularly polarized light 40 is depicted as a circle of arrows in FIG.6. The arrows represent the plane of vibration at different points intime. The circularly polarized light 40 then passes through thephotoelastic specimen 42 shown in FIGS. 1 and 6. The birefringencepresent in the photoelastic specimen creates elliptically polarizedlight 44 in which the plane of polarization rotates and the magnitude ofthe light vector changes depending on the rotational position or angle.The variation of the ellipse 46 from a mean value encodes informationabout the magnitude and direction of the principal shear stresses. Shearstresses are determined by the difference between the maximum andminimum axes of stress in the specimen.

An analyzer 24 is used to analyze the orientation and shape of theellipse 46. The analyzer 24 allows only light which is aligned with theaxis of polarization 52 to pass through to a camera 54. By rotating theanalyzer 24, the amount of light transmitted to the camera 54 assumes aperiodic function, as depicted in FIG. 4, with phase and amplitudeinformation which corresponds to shear stress intensity and orientationwithin the specimen 42. A computer 56 and/or an optical processing box(not shown) analyzes the periodic function for each of a multiplicity ofpoints on the specimen and provides a display 58 of the stresses withinthe specimen 42.

Although slow scan techniques could be used in the camera 54, thepreferred technique will use an array of detectors such as a CCD camera.The computer 56 can also process the output of each detector and,because the signal is periodic as a result of the rotating analyzer, thecomputer can perform a lock-in operation to improve the signal-to-noiseratio of the light amplitude. Further the computer can be used forcalibration and alignment as will be discussed more fully in thedescription of a particular implementation discussed below.

Description of Preferred Coating Techniques

For optimal flexibility and usefulness it is desirable to detectstresses in solid optically opaque models or real structures. Thisrequires coating the model or test structure with a birefringent coatingof known thickness. Preferably the coating will produce a birefringenceof one-quarter of a wavelength of light for a maximum stress expected inthe model. Spray-on photoelastic coating are known and are availablefrom suppliers such as Measurements Group Inc., P.O. Box 27777, Raleigh,N.C. 27611.

Conventional coatings, however, do not provide a means for determiningthe coating thickness at all points. Such a determination is necessaryfor accurate stress measurement. A preferred spray coating is formulatedto produce a coating which is of a thickness such that only a quarterwave of birefringence is produced when the maximum stress is imposed onthe coated specimen.

A dye which selectively absorbs some frequencies of light more thenothers e.g. red light, is added to a coating 59 which is coated on aspecimen 61. As shown in FIG. 14, a red ray of light 60 experiencesattenuation due to the dye in the coating 59. A blue ray of light 62experiences lesser attenuation based on the thickness of the coating. Bycomparing the relative attenuation between the blue ray of light 62 andthe red ray of light 60, the thickness of the coating on the specimen 61can be determined.

However the attenuation difference between two wavelength of light arenot sufficient to solve for coating thickness when all sources ofamplitude variation are considered. Possible sources of amplitudevariation include surface reflection from the coating, attenuationthrough the coating due to thickness, and reflection from the surface ofthe specimen. To solve for the three unknowns three equations arerequired. An additional green light ray 65 shown in FIG. 14 must beused. In actual practice the camera which receives the light passingthrough a grey field polariscope will be an red, green, blue (RGB) type.By adding one or more dyes to a photoelastic coating so that theattenuation of the three colors red, greet, blue are each substantiallydifferent, and of a known amount, the RGB camera will be able to providesufficient data to solve for coating thickness, surface of coatingreflected and reflection from the surface of the specimen.

Typical photoelastic materials are plastic and thus, over time, stressesinduced in them are removed by creep. This can make testing timecritical and make difficult the monitoring of stresses over long periodsof time. However the new techniques disclosed herein for detecting shearstresses in an object which is coated with a photoelastic material arevery sensitive and relatively little birefringence is required toproduce the desired one-quarter wave retardation between the fast andslow axes within the photoelastic coating.

This improved sensitivity allows the use of coatings which have notpreviously been recognized by the art as suitable for use inphotoelastic stress analysis. Aluminum naturally forms a thin oxide coatwhich is composed of aluminum oxide or the mineral corundum. This coatis extremely hard and exhibits sufficient birefringence that the oxideformed on bare metal, or as enhanced by the anodizing process, providesan excellent coating for determining stresses with the method of thisinvention. Aluminum oxide coatings from less then 0.001 inches to 0.003inches or more can be produced and provide the fractional wavelengthbirefringence typically by required the technique disclosed herein butof no use to classical techniques because of a lack of sensitivity. FIG.13 illustrates an aluminum substrate 64 with an aluminum oxide coating66 formed thereon.

The chemical processes for producing anodized coatings tend to result ina uniformly coated part. Further, aluminum is routinely applied tomaterial surfaces by vapor deposition with high tolerances in coatingthickness. The inherent ability to produce a uniform coating thicknessof aluminum oxide on aluminum or non-aluminum test specimens, combinedwith the high durability and resistance to creep or abrasion of suchspecimens, provides the possibility of long term monitoring of stresses.For example, a landing strut constructed of high strength steel alloycould be coated with aluminum and anodized. Periodically, or after ahard landing, induced stresses in the strut would be determined byviewing the strut with the process disclosed herein. The unloaded partwould show residual strain in the part. Testing the part while loadedwould show any change in the way the part responded to loads which couldfor example indicate a developing flaw in the part.

The technique of photoelastic stress analysis disclosed herein makespossible a wide range of coating approaches, whether chemically or vapordeposited, which have desirable properties such as durability andresistance to creep.

Examples of Specific Devices

A grey field polariscope 70 employing the principles discussed herein isshown in FIG. 2. A specimen 72 has a thin layer of photoelastic material74 formed or deposited on its surface. The specimen 72 is subjected tothe load condition for which it is desired to determine the shearstresses in the specimen 72. The polariscope 70 has a light source 76which supplies light 78 which is focused through a condenser lens 80.The light 78 passes through a rotating polarizer 82 and a corotatingone-quarter waveplate 84 which has its fast axis offset from the planeof polarization by forty-five degrees. The light 78 which is nowcircularly polarized is reflected from the specimen 72 through thephotoelastic coating 74. The stresses in the photoelastic coating 74changed the circularly polarized light into elliptically polarizedlight.

The specimen 72 is viewed by a CCD array camera 86 which looks through arotating analyzing polarizer 88. The analyzer 88, the polarizer 82 andthe one-quarter waveplate 84 can be driven by belts 90 which are drivenby a common motor 92. Because the light passing through the polarizer 82and the one quarter waveplate 84 is circularly polarized, the rate ofrotation of the analyzer need not be the same as that of the polarizerand one-quarter waveplate. However it may be advantageous if all opticalelements are rotated at a same rate so that any inconsistencies in theoptical system will not change.

The output of the CCD camera is fed to a computer 94 where a lock-in maybe performed on the periodic varying brightness of each pixel. Thelock-in can provide extremely accurate information about phase andbrightness variation of each pixel. A lock-in is a well knowncomputation technique which permits accurate analysis of time varyingsignals, such is disclosed in my U.S. Pat. No. 5,201,582 the disclosureof which is hereby incorporated by reference herein.

The phase information is directly related to the orientation of themajor axis of the elliptically polarized light received from thespecimen 72 and the magnitude of the light intensity at the maximum isproportional to the shear stress at a point on the specimen 72corresponding to a particular pixel.

FIGS. 7-12 show various optical implementations of the method of thisinvention.

The apparatus of FIG. 7 is schematic of a grey field polariscope 101similar to the polariscope 70 shown in FIG. 2. A light source 96 passeslight through a plane polarizer P a one-quarter waveplate 98 reflects aspecimen S and is viewed through an analyzer polarizer by a CCD camera100. In the optical setup of FIG. 7 only the analyzer A is required torotate because the specimen S is illuminated with circularly polarizedlight.

FIG. 8 shows a similar optical arrangement, grey field polariscope 105where the one-quarter waveplate 98 is positioned in the light path 102after the light has reflected from the specimen S. In this example allthree components of the optical system may be made to rotate. Or thepolarizer P alone may rotate.

FIG. 9 shows a compact optical system grey field polariscope 107employing a single plane polarizer P and a one-eighth waveplate 103. Thelight path 104 passes through the optical elements P and the one-eighthwaveplate 103 twice. A beam splitter 106 allows light from the source 96to be transmitted along the same optical path 104 as the camera 100observes.

Because the polarizer P acts as the analyzer, it must rotate, whichmeans the one-eighth waveplate 103 will rotate with the polarizer P.This configuration would lend itself to a compact optical instrumentwhich would illuminate and view the test specimen with a minimum ofoptical opponents and would package compactly.

FIG. 10 shows an optical system grey field polariscope 109 similar tothat shown in FIG. 7 only the specimen is a transmission specimen. Againonly rotation of the analyzer A is required for the system illustratedin FIG. 10 because the light passing through the specimen S iscircularly polarized.

FIG. 11 shows a transmission grey field polariscope 111 optical systemsimilar to the reflection optical system shown in FIG. 8.

FIG. 12 shows a transmission optical system grey field polariscope 113similar to the reflection optical system shown in FIG. 9.

A FULL FIELD SHEAR STRESS MEASURING INSTRUMENT WITHOUT MOVING PARTS

The discussion to this point assumes that at least the analyzer isrequired to rotate in order to assess the phase angle of theelliptically polarized light which is reflected or transmited from thespecimen. However this is only one way in which the orientation andshape of the elliptically polarized light from each point on a specimencan be analyzed.

Another approach is to view the elliptically polarized light reflectedfrom the specimen through at least three plane polarizers with differentorientations. As shown in FIG. 15, a grey field stress analyzinginstrument 110 of this invention utilizes beam splitters to view aspecimen 112 with four cameras at four polarizer orientations spacedforty-five degrees apart.

The instrument 110 has a housing 114 which houses a light source 116which passes through a lens 118 to project a beam of parallel rays. Thebeam is reflected off a mirror 120 through a plane polarizer 122 and aone-quarter waveplate 124. The circularly polarized light thus createdis directed by a non-polarizing beam splitter 126 through an opticalelement represented by lens 128 which projects the light onto thespecimen 112 and receives light which is imaged by the four cameras. Thecircularly polarized light is thus projected onto the specimen 112.Reflected light passes through the same optical element formed by thelens 128 passes straight through the beam splitter 126. An additionallens 130 and an aperture stop 132 provide a clean image to a second beamsplitter 134. The second beam splitter 134 splits the light into twoidentical beams. One beam is directed through a one-half waveplate 136which effectively rotates the light passing through it forty-fivedegrees. The light passing through the one-half waveplate 136 enters afirst polarizing beam splitter 138 which splits the light into twoorthogonal polarized beams. Each beam is then imaged by a CCD array 141in each camera 140 and 142.

The light which does not pass through the one-half waveplate 136similarly is split by a second polarizing beam splitter 144. The outputof the second polarizing beam splitter 144 is viewed by a third camera146 and a fourth camera 148. Hence four cameras 140, 142, 146, 148simultaneously view the same test specimen 112. The third camera 146views the specimen 112 through a polarized filter which is orientedbetween the polarized light viewed by the first and second camera 140,142. The light through the fourth camera 148 is one-hundred andthirty-five degrees away from the angle of polarization of the firstcamera.

The instrument 110 efficiently utilizes the light received from the testspecimen. Essentially all the light received by the instrument 110 fromthe test specimen 112 is received by the four cameras which have highquantum-efficiency CCD array detectors. The polarizing beam splitters138, 144 efficiently split the light passing through them into two beamswithout blocking any light. The polarizing beam splitters are notcompletely efficient and, for example, a small percentage of the lightwhich passes to the first camera 140 is not polarized in the desiredplane. Thus plane polarizers 150 are positioned in front of each camerato clean up the light passing through each side of the beam splitters.

An additional polarizer 160 may be positioned in front of each camera tobalance the amount of light passing into each camera. However, balancingthe intensity of each image is probably better performed in the computermanipulation of the output of the CCD.

If rotating components are eliminated the problem which may beassociated with rotating, such as vibration, wear, maintenance can beeliminated. The grey field instrument 110 splits the light reflectedfrom the structure 112 so it can be viewed through four analyzer eachoriented forty-five degrees apart. This provides four samples whichcould be gotten sequentially by sampling light passing through arotating analyzer. With a rotating analyzer many discrete images areobtained and processed to extract the required information concerningthe brightness variations of the sample as viewed through a grey fieldpolariscope. Because the output signal is a simple sine function foursamples are sufficient to characterize the brightness variation on thestructure 112. However if necessary additional beam splitters combinedwith one-half waveplates could provide as many samples as necessary tocharacterize the elliptically polarized light received from thestructure 112.

The alignment of the instrument 110 is quite simple. A standard testpattern is placed in the field of view and the images obtained by thefour cameras can be aligned electronically. With the size of modern CCDarrays and the required resolution of shear stresses within thespecimen, a considerable excess in detector capability and resolutionexists so that the cameras may be aligned by correlating the illuminatedCCD elements with the test pattern. This simple computer alignment whichcould be performed manually or by an automatic computer routine may becontrasted with the difficulty of aligning instruments which utilizeinterferometry photoelastic techniques.

A computer (not shown) alone or combination with a specializedelectronics box receives the output of the CCD cameras and processes theoutput of the CCD to determine the shear stresses imaged by theinstrument 110. The computer (not shown) may also control any automatedfeatures of the instrument 110. The computer performs the necessarycalibrations of the CCD arrays including compensating for alignment andoptical effects.

The grey field polariscope 110 can be rapidly and repeatedly calibratedelectronically. Not only in alignment and sensitivity of each sensor ineach camera but also in its proper ability to measure birefringence. Forexample a silvered one-eighth waveplate on which the fast and slow axesare labeled can be imaged and any defect or variation in the optics ofthe polariscope 110 checked and zeroed out. In addition, the orientationof the maximum shear stresses can be checked again the one-eighthwaveplate with its clearly labeled optical axes. The grey fieldpolariscope is not only an extremely sensitive instant but one which isinherently easily calibrated and aligned. The calibration device such asa one-eighth waveplate does not have to be silvered but can be placed infront of a mirror or other reflective but birefringent free surface.

It is important that an instrument which will be used by engineers as atool in the field as well as the laboratory be amenable to setup andalignment procedures which are not excessively rigorous or taxing. Theinstrument 110 provides the compact packaging, self alignment andcalibration necessary in a device which will be used in everyday design,test, and maintenance situations. Further during long term tests, theability to check calibration periodically without moving the instrument110 or making any mechanical adjust improves the reliability of the datacollected.

The light received by the four cameras 140, 142, 146, 148 can beaveraged to give the total flux from each discrete area on the model.This allows correction for non-uniformity of the illuminating light.Further it allows correction for model dependent characteristics such asan off axis viewing of three dimensional surfaces. If three color CCDarray cameras are used the total light flux in each color from eachdiscrete area on the model can be determined and used to calculate thethickness of a coating wavelength dependent attenuation of light asdiscussed above.

The grey field polariscope 110 because it takes sufficient images todetermine shear stresses simultaneously can operate at high speeds. Aflash lamp for example could provide sufficient light to freeze theshear stresses in the anodized coating aluminum plate which is beingimpacted by a bullet. And imaging can be performed on components ofdynamic structures. For example the stresses in a turbine blade causedby centrifugal forces can be image while the blade rotates.

The grey field polariscope 110 while providing the desirable feature ofproviding full field shear stress images of static structures can beused to provide continuous imaging of dynamic structures. A lock-in onthe dynamic images can provide an image of peak dynamic shear stresses.

An additional function which can be incorporated into the method ofstress analysis disclosed herein is to view the specimen through therotating analyzer alone while the specimen is illuminated withnon-polarized light. A single rotating plane polarizing filter willproduce changes in model brightness only if reflected light has beenpolarized by the model or any coatings thereon. The well known use ofpolarizing glasses to reduce glare illustrates the polarization of lightcaused by reflection. This type of polarization can be mistaken forbirefringence with standard analysis techniques.

By first viewing the object and determining the amount of polarizationinduced by reflection such induced polarization can be subtracted fromthe results produced when the specimen is illuminated with circularlypolarized light. With this technique higher resolution is possible.

Additionally the polarization data can be used to determine an angle ofincidence between the light beam and the model which can lead to theability to image shear stresses on complicated models. Typically withconventional stress analysis off angle viewing is limited to about 10degrees. With the technique of this invention, considerably greateroblique viewing may be possible.

The instrument 110 shown in FIG. 15 can determine non-photoelasticinduced polarization without rotating the analyzer by simply providingfor the polarizer 122 and one-quarter waveplate 124 to be manually orautomatically removed from the light path between the light source 116and the specimen 112.

Likewise the instrument 70 in FIG. 2 can incorporate this feature byallowing the polarizer 82 and one-quarter waveplate 84 to slide or swingout of the light path 78. The embodiment shown in FIG. 9 requires onlythe removal of the one-eighth waveplate 103. It is therefore easilyarranged in all the various embodiments to remove the optical elementswhich generate the circularly polarized light so that the specimeninduced polarization can be determined and subtracted from the stressanalysis images.

Another approach to correct for reflection induced polarization is toimage the photoelastic coating with both left- and right-handedcircularly polarized light. By adding the images thus produced theeffects of reflection-induced polarization are eliminated and intensityof the stress induced birefringence is doubled. The direction ofrotation of the circularly polarized light is controlled by the angularplacement of the fast axis of the one-quarter wave plate with respect tothe axes of polarization of the first polarizer. Thus by changing theorientation of the one-quarter wave plate by ninety degrees, fromforty-five degrees to the right of the polarizer axis, to forty-fivedegrees to the left of the polarizer axis, the rotation of thecircularly polarized light is reversed. Rotating the one-quarterwaveplate is even simpler to implement than removing the one-quarterwave plate and the polarizer from the optical path.

It should be understood that any mathematical lock-in algorithm can beused to increase the sensitivity of the instruments to the brightnesschanges on the model which are due to induced birefringence. It is alsopossible to filter the four images produced by the instrument 110 toextract only those variations between images which are consistent withthe underlying physical phenomenon. It is also apparent that additionalimages taken at other angles could be incorporated in the instrument 110and that if sufficient images are taken they approach a continuousrotating analyzer for purposes of performing lock-in on the brightnessvariations present in the specimen.

The method of photoelastic stress analysis discussed herein can be usedwith multiple fringe stresses in coatings on test specimens. Increasingthe load on the specimens gradually while repeatedly performing fullfield analysis allows computer tracking of the shear stress informationbetween or in front of fringe lines as they develop and move across thespecimen. Thus the sub fringe technique disclosed herein is a specialcase of a more general technique which employs a lock-in algorithm andtracks sub fringe brightness changes as a specimen is loaded todetermine stresses within a specimen.

Although most applications of the disclosed photoelastic stress analysistechnique will employ models or specimens with coated surfaces there arespecialized uses for transmission specimens. For example a process suchas shown in FIGS. 10 through 12 could be used to detect residualstresses in glass. For example the weak birefringence in automobilewindows is ideal for determining residual stresses in the windows asmanufactured by a sub fringe transmission technique.

The techniques and apparatuses disclosed herein for analyzing theelliptically polarized light are directed to determining the variationin intensity between the average intensity and the minimum and maximumintensity. This is illustrated in FIG. 4 where a two ω plot 162 of lightintensity is shown. This is in contrast to earlier techniques whichproduced a four ω plot such as shown in FIG. 3 or produced outputs whichcombined four ω signals with two ω signals. Further, earlier techniquesinvolved solving for the absolute magnitude of the axes of the ellipsewhereas the techniques disclosed herein require finding only thedifference between an elliptically, or preferably circularly, polarizedreference, and an observed elliptically polarized light.

Many techniques are available for finding this variation in brightnessand its phase angle β shown in FIG. 4. If the analyzer is rotating, alock-in algorithm may be employed which is basically related toconsidering the signal in the frequency domain by, for example,employing a Fourier transform. Other techniques which use theperiodicity of the signal to better extract the desired informationcould be used. Further, where a device such as the instrument 110 shownin FIG. 15 is employed, the extraction of the signal is a mathematicaloperation on the four images obtained which assumes the signals aresinusoidal and four samples of that signal are available for processing.And it is understood that the claims are not limited to a particularsignal processing algorithm or technique but are directed generally tothe process of obtaining multiple images and extracting the informationconcerning brightness variation and phase which correlates with maximumshear stress magnitude and orientation.

It should be understood that the photoelastic effect is produced bystrain in the photoelastic material and, because the determined value,i.e. the difference between the fast and slow axes in the photoelasticmaterial, is directly proportional to the shear stresses in thematerial, for simplicity the description speaks to the observation ofshear stresses, although physically only strain produces observablephenomenon.

It should be understood that a monochromatic light source may be used orwhite light they be used in any of the grey field polariscopes describedherein.

It should be understood that circularly polarized light is a specialcase of elliptically polarized light where the eccentricity of theellipse is zero. And It should be understood that practical opticalcomponents will not produce perfectly circular polarized light.

It is understood that the invention is not limited to the particularconstruction and arrangement of parts herein illustrated and described,but embraces such modified forms thereof as come within the scope of thefollowing claims.

I claim:
 1. An apparatus for determining shear stresses in abirefringent material comprising: an elliptically polarized light sourcefor projecting light on to a birefringent material; an optical elementaligned with the light source so as to receive light from the lightsource after the light has passed through the birefringent material; abeam splitter in light-receiving relation with the optical element, thebeam splitter providing a plurality of light paths to a plurality ofimaging sensor arrays; and a means disposed along each of said pluralityof light paths, for linearly polarizing with different orientation thelight passing along each of said paths.
 2. The apparatus of claim 1wherein the elliptically polarized light source provides circularlypolarized light.
 3. The apparatus of claim 1 wherein the optical elementboth projects light from the source and receives light from abirefringent material.
 4. The apparatus of claim 1 wherein the beamsplitter comprises a first beam splitter in light providing relationshipwith a first polarizing beam splitter, and a one-half wave platefollowed in light receiving relationship by a second polarizing beamsplitter, and wherein the first polarizing beam splitter provides twolight paths, and the second polarizing beam splitter provides two lightpaths and the first and second polarizing beam splitters provide themeans for polarizing light.
 5. An apparatus for measuring stresses in anobject comprising: a source of circularly polarized light; an objecthaving a birefringent coating intimately attached on a surface of theobject; the surface being illuminated by the source of circularlypolarized light; an analyzer system positioned to receive light from thesource reflected off the object and passing through the birefringentcoating on the object, the analyzer having a beam splitter and aplurality of cameras each receiving similar images of the object,wherein each camera has a digital array on which the image of thesurface of the object is projected, each digital array having anassociated linear polarizing filter of a different orientationpositioned in front of said digital array; and a computer receiving datafrom each digital array and processing said data to determineorientation and magnitude of stresses in the object.
 6. A stressanalyzing instrument comprising: a housing; a light source mounted tothe housing; a first lens which projects light from the light source ina beam of parallel rays; a first plane polarizer mounted to the housingand receiving said beam of parallel rays; a first one-quarter waveplatemounted to the housing to receive the beam parallel rays passing throughthe first plane polarizer to create a beam of circularly polarizedlight; a non-polarizing first beam splitter mounted to the housing toreceive the beam of circularly polarized light and to direct a projectedbeam which is emitted from the housing and onto a specimen, wherein areflected light beam returned by the specimen enters the housing andpasses through the first beam splitter; a second beam splitter mountedto the housing to receive the reflected beam passing through thenon-polarizing first beam splitter, wherein the second beam splittersplits said reflected beam of light into a first split beam and a secondsplit beam; a first one-half waveplate mounted to the housing whichreceives said first split beam; a first polarizing beam splitter mountedto the housing to receive the first split beam exiting the firstone-half waveplate, being thereby split into a first and a secondorthogonal polarized beam; a first camera positioned to image said firstpolarized beam; a second camera positioned to image said secondpolarized beam; a second polarizing beam splitter mounted to the housingto receive the second split beam from the second beam splitter, thesecond polarizing beam splitter producing a third and a fourthorthogonal polarized beams; a third camera mounted to the housing toimage said third orthogonal polarized beam; a fourth camera mounted tothe housing to image said fourth orthogonal polarized beam, the fourcameras simultaneously viewing said specimen; and a controller receivingdigital images from said first, second, third, and fourth cameras, andprocessing said images to generate an image of the stresses in thespecimen.
 7. The stress analyzing instrument of claim 6 furthercomprising: a second lens mounted to the housing to receive thereflected beam exiting the first beam splitter; and an aperture stopmounted to the housing to receive the reflected beam exiting the secondlens ahead of the second beam splitter.
 8. The stress analyzinginstrument of claim 6 further comprising plane polarizers positioned infront of each camera to clean up the light passing through each side ofthe beam splitters.
 9. The stress analyzing instrument of claim 6,further comprising an optical element mounted to the housing throughwhich the projected beam is directed from the housing onto an analyzedobject.
 10. A method of determining the stresses in a transparentbirefringent object comprising the steps of: passing ellipticallypolarized light through a birefringent object; obtaining multipledigital images of the elliptically polarized light transmitted throughthe object wherein each digital image is taken through a linearpolarizing filter of different orientation; analyzing the multipledigital images in a digital computer to determine the variation ofelliptically polarized light transmitted through each of a multiplicityof discrete portions of the object and the phase of said transmittedlight; and calculating the stress at each discrete portion of thesurface from the determined variation and phase of said transmittedlight from each discrete portion of the surface of the object.
 11. Themethod of claim 10 wherein the elliptically polarized light iscircularly polarized.
 12. A method of determining weak birefringence inglass comprising the steps of: passing elliptically polarized lightthrough glass; obtaining multiple digital images of the ellipticallypolarized light transmitted through a multiplicity of discrete areas ofthe glass wherein each digital image is taken through a linearpolarizing filter of different orientation; analyzing the multipledigital images in a digital computer to determine variations inamplitude of the elliptically polarized light transmitted from each ofthe multiplicity of discrete portions of the surface of the object andthe phase of said variations in amplitude of the elliptically polarizedlight; and providing a display of the stresses within the specimen. 13.The method of claim 12 wherein: the glass is an automobile window, andwherein residual stresses arising from the manufacture of the automobilewindow is detected.
 14. A stress analyzing instrument comprising: alight source, producing a beam of light; a first polarizer; a secondpolarizer; a means for rotating at least the second polarizer at aselected angular rate; one and only one one-quarter wave platepositioned between the first polarizer and the second; a camera with anarray of light detecting sensors; wherein the beam of light is directedthrough the first polarizer and directly or after reflection passesthrough the second polarizer and the one-quarter wave plate and onto thearray of light detecting sensors; and a means for analyzing the lightdetected by each sensor in the sensor array to determine amplitudevariations in light and phase relationship of the amplitude variationsin received light in relation to the selected angular rate of the secondpolarizer.